High-Q lasing via all-dielectric Bloch-surface-wave platform

Controlling the propagation and emission of light via Bloch surface waves (BSWs) has held promise in the field of on-chip nanophotonics. BSW-based optical devices are being widely investigated to develop on-chip integration systems. However, a coherent light source that is based on the stimulated emission of a BSW mode has yet to be developed. Here, we demonstrate lasers based on a guided BSW mode sustained by a gain-medium guiding structure microfabricated on the top of a BSW platform. A long-range propagation length of the BSW mode and a high-quality lasing emission of the BSW mode are achieved. The BSW lasers possess a lasing threshold of 6.7 μJ/mm2 and a very narrow linewidth reaching a full width at half maximum as small as 0.019 nm. Moreover, the proposed lasing scheme exhibits high sensitivity to environmental changes suggesting the applicability of the proposed BSW lasers in ultra-sensitive devices.


Design of the dielectric multilayer sustaining the Bloch surface waves (BSWs).
The dielectric multilayer sustains BSW modes at wavelengths of the lasing band from R6G-doped SU-8 ring lasers. In this work, a BSW platform consisting of five pairs of alternating TiO 2 (high refractive index, n = 2.31) and SiO 2 (low refractive index, n = 1.46) layers was designed for the wavelength of 580 nm. The layer respective thicknesses d are calculated based on the equation 26 : where λ is the designed wavelength, n the refractive index, and θ the refraction angle of light within the TiO 2 and SiO 2 layers, respectively. According to this equation, the thicknesses of TiO 2 and SiO 2 layers are 71 and 154 nm, respectively, which are designed at refraction angle θ of 50° within the  Supplementary Figures 3a-c, the n effective , k effective , and the confinement factor of these three guided modes all exhibit a weak dependence when the ridge width is larger than 1 μm. When the ridge width is further decreased, they demonstrate different behaviors.
For the photonic mode, a mode cutoff, where the confinement factor drops rapidly, can be observed when the ridge is smaller than 700 nm. For the hybrid plasmonic mode, on the other hand, good optical confinement over the ridge width is obtained. Furthermore, for the BSW mode, the confinement factor starts to decrease rapidly when the ridge width is smaller than 800 nm, and the k effective (corresponding to propagation loss) increases from 10 −4 to10 −3 . In Supplementary Figure 3b, an important feature worth noticing is revealed: the BSW mode experiences smaller propagation loss (k effective ) than the hybrid plasmonic mode for a range of the ridge width from 0.5 to 2.5 μm, indicating an important advantage of the BSW-based devices for long-range light propagation. FWHMs are slightly larger than the spectrometer spectral resolution.

Discussion of the group index of the BSW lasers
The group index n g of the BSW lasers is theoretically calculated from the BSW dispersion diagram (Supplementary Figure 9a) and is compared to the experimentally determined value. Here, the BSW dispersion was obtained using the mode analysis. The group index is defined as the ratio of the velocity of light in vacuum (c) to the group velocity (v g ) for the BSW mode. The group velocity v g is expressed by: which can be directly obtained from the slope of the BSW dispersion. Accordingly, the group index n g of the BSW laser is calculated to be 1.83 from the definition n g = c/v g , and this value agrees well with the experimentally determined group index of 1.82.
For comparison purposes, the group index n g of the photonic lasers is also theoretically and

Detailed discussions about the verification of the BSW lasing
To investigate the complete BSW modes, the modes sustained by the proposed BSW laser structure have been comprehensively investigated. In the following simulation results, the BSW laser structure geometry was obtained from SEM images of the fabricated devices, which comprises five pairs of alternating TiO 2 and SiO 2 layers having respective thicknesses of 82 and 170 nm (as the BSW platform), and a R6G-doped SU-8 ridge having a thickness of 136 nm (as the top guiding structure with the oblique sidewall) lying onto the surface of the BSW platform.
Since the width of the ridge waveguide is greater than or equal to 1.5 μm, the higher-order BSW modes indeed exist in the structure and they are investigated using mode analysis. Supplementary

Investigation into the BSW lasing mode by leakage radiation microscopy
The BSW lasing mode was investigated by leakage radiation microscopy 28

Detailed discussions about the Q leak of the BSW ring cavities
The Q leak of the BSW ring cavities for the ridge with non-vertical sidewalls as a function of width for different diameters were simulated, using eigenfrequency analysis for an axisymmetric model, and compared the results with the Q leak-surr , as displayed in Supplementary Figures 16a-d Note that these distributions of the WGM modes are pushed outward in the radial direction, and the distribution becomes smaller with decreasing diameter due to the effect of the curvature. When the ridge width further decreases from w = 2.5 μm, the WGM modes are still supported by the ring cavity and the distributions remain the same. In this case, the Q leak is independent of the ridge width, suggesting that the Q leak is evaluated by only considering the WGM mode distribution in the eigenfrequency analysis. When the ridge width is decreased until the inward ridge edge becomes close to the WGM mode distribution, then the Q leak-surr becomes comparable to the Q leak . A further decrease in the ridge width results in a mode distribution with an electric field distribution similar to that of a guided BSW mode within a ridge waveguide (see Supplementary Figures 16i and 16j), and the Q leak is found to be similar to the Q leak-surr for small ridge widths. According to these results, we conclude that the simulated Q leak using eigenfrequency analysis for an axisymmetric model

Investigation of multilayer design for the BSW laser
From the dispersion diagram of the BSW mode (Supplementary Figure 2), one can assume that the BSW mode wavevector will become larger when designing the multilayer for a red-shifted forbidden band. Also, a BSW mode in the lasing band could still be sustained within a SU-8 polymer  (Figure 5a), implying that the lasing thresholds of the revised design should be limited by other losses than the leakage-related losses (losses from the effect of curvature and propagation) such as the surface scattering losses. Importantly, it is found that the lasing threshold value is significantly reduced to 33% of that of the original design for the BSW laser with a diameter of 30 μm, which is attributed to the decrease in leakage-related losses.
Furthermore, the minimum diameter achieving lasing is shrunk to 20 μm (Supplementary Figure   20e). According to these results, we confirmed that the lasing performance of the BSW lasers could be improved using a better design of the BSW platform.

Coupling between a BSW ring laser cavity and a waveguide
To demonstrate the possibility of using the BSW laser for optical integrated circuits, we have investigated the coupling between a BSW ring laser cavity and a waveguide using the finite-

Photobleaching of the BSW lasers made of R6G-doped SU-8 polymer
The photobleaching of the BSW lasers is investigated by continuously pumping laser devices and collecting their emission intensities. Photobleaching is a common photo-induced degradation for dye molecules. When exposed to intense light, the local heating near the dye molecules during pumping enables them to receive mobility and then react with the polymer matrix, the impurities (e.g., oxygen), or the other dye molecules, resulting in degradation of the fluorescent dyes 19 .
Supplementary Figure 22 shows the normalized emission intensity of a BSW laser (D = 100 μm) as a function of the number of pump pulses. The emission intensity decreases to half of its initial value after approximately 20,000 pulses. Note that this lifetime is of a similar order of magnitude as that reported for R6G-doped SU-8 polymer lasers 19,32 . Although the photobleaching of dye-doped polymer restricts the lifetime of the proposed BSW laser, the fabrication method is simple, cheap, and rapid, making it suitable for large production. Furthermore, the photobleaching can be reduced by operating the laser at low temperature 33 , working under an inert atmosphere 33 , or filling the free volume in the polymer host with additives (such as diphenyl thiourea 34 ) could improve the photostability of such BSW lasers and make them more favorable in long-term applications. It is also noted that the R6G-doped SU-8 polymer was chosen as the gain medium in this study to provide a proof of concept for the BSW laser. We believe that the applicability of the proposed BSW laser can be drastically extended by employing an inorganic gain medium (e.g., Er-doped Si and GaN) so that the biosensing applications of the BSW lasers will be made possible.
Supplementary Figure 22. The normalized emission intensity of the BSW laser as a function of the number of pump pulses. The diameter of the BSW laser was 100 μm and the pump energy density 10.9 μJ/mm 2 .

Environmental sensitivity investigation of the BSW lasers
Before investigating the environmental sensitivity of the BSW lasers, we first investigated the interaction between the SU-8 polymer and toluene vapor using a quartz crystal microbalance (QCM) 35 detection system to clarify the sensing mechanism for the SU-8 polymer. The well-known detection mechanism of QCMs relies on the shift of the resonance frequency of a quartz crystal resonator (QCR) upon deposition of a thin film on one of the sides of the quartz crystal. Transversal oscillation modes (e.g., breathing modes) are used to reduce interaction with the atmosphere just above the quartz crystal and thus realize a high-quality factor of resonance that enables high sensitivity to the thickness of deposited layers onto the quartz crystal. polymer-coated QCR is removed from the toluene vapor, we infer that both sorption of toluene vapor and sorption followed by swelling should be the possible contributions when SU-8 polymer is exposed to toluene vapor.
To fully rule out any effect of condensation on the SU-8 polymer, the QCM system was connected to a water chiller that was used to control the temperature of the QCRs (the temperature was set to 12°C). The temperature-controlled QCRs were then exposed to toluene vapor to observe the condensation of toluene gas molecules onto the surface of the QCRs, as shown in Supplementary The environmental sensitivity of the proposed BSW lasers is then investigated by monitoring the lasing wavelength in the presence of toluene vapor. The experimental details are described as follows. First, the BSW laser sample was placed inside a chamber connected to a cylinder with its gas valve closed. A droplet of 50 μL toluene was added inside that cylinder beforehand. After optically pumping the BSW laser sample, the system was maintained with the valve closed for 60 min to obtain saturated vapor of toluene, and then the BSW laser sample was optically pumped again to check the stability of the structure. Next, the gas valve was opened so that the saturated vapor of toluene started to diffuse into the chamber. Once the toluene molecules reached the BSW laser, they could just sorb onto the surface or sorb and then diffuse into the R6G-doped SU-8 polymer ridge and thereby swelled the structure. Then, the emission spectra of the BSW laser as a function of time were collected for studying the sensitivity of the BSW lasers (Figure 6b). Regarding the investigation of the swelling effect, it should be noted that the simulated values for the changes that can explain the lasing shifts are of the same order than those measured for the